Question

use the line segments to connect all possible pairs of the points a, b, c, and d. then complete the statement below.

Explanation:

Step1: Use combination formula

The number of ways to choose 2 points out of $n$ points to form a line - segment is given by the combination formula $C(n,2)=\frac{n!}{2!(n - 2)!}=\frac{n(n - 1)}{2}$. Here $n = 4$.

Step2: Calculate the result

Substitute $n = 4$ into the formula: $C(4,2)=\frac{4\times(4 - 1)}{2}=\frac{4\times3}{2}=6$.

Answer:

6 line - segments can be formed by connecting all possible pairs of the 4 points A, B, C, and D.